A certified basis of 13 identities
This list of identities is a basis, proved in Lean, of 11 semigroups of order six, all of which generate the variety V[4053]. Removing the identities that follow from the others leaves 5 identities (Vampire); the variety page shows the shortest known basis.
Identifier sb-3934e08097bd819e in the data of the bases-min seal.
Certified for
[6, 4053] [6, 4059] [6, 4157] [6, 4163] [6, 4265] [6, 4271] [6, 6246] [6, 6269] [6, 6282] [6, 6284] [6, 6858]
The identities
- x² ≈ x⁴
- x³yx ≈ xyx
- x²yx ≈ xyx²
- x²yx² ≈ xyx
- x²y² ≈ xyxy
- x²y² ≈ xy²x
- x²y² ≈ yx²y
- xyx ≈ xyx³
- x³y² ≈ yx³y
- x²yz ≈ xyxz
- x²yzy ≈ xy²zx
- x²yzy ≈ yx²zy
- x²yz² ≈ xyz²x